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Large-range constant threshold growth model in one dimension


 
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1. Title Title of document Large-range constant threshold growth model in one dimension
 
2. Creator Author's name, affiliation, country Gregor Sega; Faculty of Mathematics and Physics, University of Ljubljana
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) growth model; asymptotic propagation velocity; invariant distribution
 
3. Subject Subject classification 60k35;82b23;82c22
 
4. Description Abstract We study a one dimensional constant threshold model in continuous time. Its dynamics have two parameters, the range $n$ and the threshold $v$. An unoccupied site $x$ becomes occupied at rate 1 as soon as there are at least $v$ occupied sites in $[x-n, x+n]$. As n goes to infinity and $v$ is kept fixed, the dynamics can be approximated by a continuous space version, which has an explicit invariant measure at the front. This allows us to prove that the speed of propagation is asymptoticaly $n^2/2v$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-01-27
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/598
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-598
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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